中文摘要：

该文首先构造了耦合的mKdV方程的新的达布变换,同时显式给出了它的达布矩阵T_N和新解q^[N],r^[N）的行列式表示.其次,考虑将约化条件r=q^＊附加到该达布变换上,以及考虑一个周期的非零种子解,得到了散焦mKdV方程的N重暗孤子解的行列式表示.最后,证明了暗的单孤子解和暗的2孤子解是光滑的,进一步证明了暗的N（N≥2）孤子解至少在某一邻域内是光滑的.

英文摘要：

For coupled modified Korteweg-de Vries （mKdV） equation, we construct a new Darboux transformation （DT）, whose Darboux matrix TN and transformed solutions q^[N] r^[N] are explicitly given in determinant form. When the reduction condition r = q^＊ is imposed on the new DT and a periodic non-zero seed solution is considered, we obtain determinant representation of dark N-soliton solutions for the defocusing mKdV equation. Especially, we show that dark 1-soliton and dark 2-soliton are both smooth solutions, and furthermore, we show that dark N-soliton solutions are smooth at least on a certain domain.